Score Function
المؤلف:
Rodriguez, G.
المصدر:
"Lecture Notes on Generalized Linear Models." 2007. https://data.princeton.edu/wws509/notes/.
الجزء والصفحة:
...
10-2-2021
1461
Score Function
The score function 
is the partial derivativeof the log-likelihood function 
, where 
is the standard likelihood function.
Defining the likelihood function
 |
(1)
|
shows that
 |
(2)
|
and thus that
Using the above formulation of 
, one can easily compute various statistical measurements associated with 
. For example, the mean 
can be shown to equal zero while the variance is precisely the Fisher information matrix. The score function has extensive uses in many areas of mathematics, both pure and applied, and is a key component of the field of likelihood theory.
REFERENCES:
Rodriguez, G. "Lecture Notes on Generalized Linear Models." 2007. https://data.princeton.edu/wws509/notes/.
Sun, D. and Xiao, F. "Likelihood Theory with Score Function." 2013. https://www.stats.uwo.ca/faculty/bellhouse/Likelihood_Theory_with_Score_Function.pdf
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